Kinetic Isotope Effects and Hydrogen Tunnelling in PCET Oxidations of Ascorbate: New Insights Into Aqueous Chemistry?

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Review Kinetic Isotope Eﬀects and Hydrogen Tunnelling in PCET Oxidations of Ascorbate: New Insights into Aqueous Chemistry?

Ana KarkovićMarković,Cvijeta JakobušićBrala * , Viktor Pilepićand Stanko Uršić*

Faculty of Pharmacy and Biochemistry, University of Zagreb, A. Kovaˇci´ca1, 10 000 Zagreb, Croatia; [email protected] (A.K.M.); [email protected] (V.P.) * Correspondence: [email protected] (C.J.B.); [email protected] (S.U.); Tel.: +385-01-4870-267 (C.J.B.)

Academic Editor: Poul Erik Hansen Received: 17 February 2020; Accepted: 21 March 2020; Published: 23 March 2020

Abstract: Recent experimental studies of kinetic isotope eﬀects (KIE-s) and hydrogen tunnelling comprising three proton-coupled electron transfer (PCET) oxidations of ascorbate monoanion, (a) in aqueous reaction solutions, (b) in the mixed water-organic cosolvent systems, (c) in aqueous solutions of various salts and (d) in fairly diluted aqueous solutions of the various partial hydrophobes are reviewed. A number of new insights into the wealth of the kinetic isotope phenomena in the PCET reactions have been obtained. The modulation of KIE-s and hydrogen tunnelling observed when partially hydrophobic solutes are added into water reaction solution, in the case of fairly diluted solutions is revealed as the strong linear correlation of the isotopic ratios of the Arrhenius prefactors Ah/Ad and the isotopic diﬀerences in activation energies ∆Ea (D,H). The observation has been proposed to be a signature of the involvement of the collective intermolecular excitonic vibrational dynamics of water in activation processes and aqueous chemistry.

Keywords: kinetic isotope eﬀects; ascorbate PCET reactions; hydrogen tunnelling; water vibrational dynamics; activation processes

1. Introduction The aim of this review is to present the main results of our recent experimental studies of kinetic isotope eﬀects (KIE-s) and hydrogen tunnelling in some proton-coupled electron transfer (PCET) reactions of ascorbate monoanion in aqueous reaction solutions and in the mixed water-organic cosolvent systems. The issues of KIE-s and hydrogen tunnelling [1–9] and PCET reactions [10–15] are well elaborated in many relevant books and publications. The phenomenon of PCET [10–15] is ubiquitous throughout chemistry and biology. Hence, the study of KIE-s in PCET reactions is of importance not only for understanding PCET reactions in solution; above all, many enzymatic reactions involve PCET as well. However, to the best of our knowledge, there are no systematic studies of solvent inﬂuences on KIE-s and hydrogen tunnelling in PCET reactions [16]. We have investigated KIE-s and hydrogen tunnelling in the following PCET oxidations of ascorbate: (a) reaction with 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO radical) [17,18], (b) reaction with hexacyanoferrate(III) ions [19–22] and (c) reaction with ferricinium cation [22] in aqueous solutions containing substantial concentrations of organic solvents or salts. Furthermore, KIE-s and hydrogen tunnelling in reaction of ascorbate with hexacyanoferrate(III) ions have been investigated in a series of fairly diluted aqueous solutions containing small concentrations of the partially hydrophobic solutes [23]. These studies gave some new and surprising insights about KIE-s in the PCET reactions. Moreover, the studies could be in support of the recently proposed [24–27] involvement of the vibrational water dynamics [24–33] in activation processes in aqueous chemistry.

Molecules 2020, 25, 1443; doi:10.3390/molecules25061443 www.mdpi.com/journal/molecules Molecules 2020, 25, 1443 2 of 16

2. Kinetic Isotope Eﬀects and Hydrogen Tunnelling in Proton-Coupled Electron Transfer Reactions

2.1. Proton-Coupled Electron Transfer Reactions Proton-coupled electron transfer, as generally accepted today, is broadly defined as any process which includes a transfer of an electron and a proton. In these reactions, an electron and a proton can be transferred between the same or different sites, in the same or in different directions, by concerted or stepwise mechanisms. PCET also includes processes in which protons modulate the electron transfer process even if they themselves do not transfer [10–13]. The term PCET was introduced for the first time by T. J. Meyer in 1981, for reactions of ruthenium-oxo complexes, where a proton and electron are transferred in a single, concerted step. Throughout this review, we discuss concerted PCET reactions, denoted as PCET. In concerted PCET reactions the electron and proton transfer “together”, in a single kinetic step, thus circumventing high energy intermediates which would be formed in the case of stepwise mechanism [34]. Reactions in which the electron and proton transfer between the same sites are denoted as hydrogen atom transfer (HAT), and between different sites as multiple-site concerted proton-electron transfer (MS-CPET) [12]. Concerted PCET is an important mechanism for charge transfer in a wide variety of biological processes, such as photosynthesis, respiration and many enzymatic reactions, as well as chemical and electrochemical processes, particularly those relevant to solar cells and other energy devices [7,10–14,35–43]. The long-distance transfer of electrons in biology often exhibits the characteristics of PCET. Inspired by the photosynthetic photosystem II, which utilizes solar energy and catalyses water splitting reaction, a variety of solar energy devices have been developed. One of the first developed molecular catalysts was Ru “blue dimer” [10]. Today, great attention is directed toward the design of various metal-based catalysts, electrocatalysts, multiproton relays, nanoparticle catalysts [14,44]. One example is Dye Sensitized Photoelectrosynthesis Cell which combines the properties of wide bandgap semiconductor nanoparticle oxides and the light absorption/catalytic properties of the chromophore–catalyst [45]. Recently, it was observed that excited-state PCET reactions can access the Marcus inverted region, which is of great importance in the development of solar energy technologies [15,46,47]. In addition, it opened the intriguing question about the role of inverted region in biological pathways [48]. Moreover, the applications of PCET in organic synthesis and drug discovery have attracted great attention in recent years [38,49–52]. PCET reaction enabled a new route in the production of ammonia, one of the most important industrial processes [53]. In addition to these complex processes, the investigation of simpler model systems is also important for investigating the fundamental physical principles underlying PCET reactions [10–12]. Recently, the first examples of MS-CPET for the activation and formation of C H bonds have been reported [12,49,50]. − To understand complex physical properties of PCET reactions, a combined experimental and theoretical approach is essential. The theory for PCET reactions mostly developed by Hammes-Schiffer group combines the concepts from Marcus theory for electron transfer and analogous theories for proton transfer [13,34,35,54]. The theory describes PCET reaction in terms of vibronically nonadiabatic transitions including the effects of thermal fluctuations of the solvent or protein environment, and the proton donor-acceptor motion. The theory differentiates between HAT and MS-CPET regarding the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic and MS-CPET to electronically nonadiabatic proton transfer. Within the framework of the theory, a series of rate constant expressions have been derived for PCET reactions in different regimes. The simplest expression for rate constant of vibronically nonadiabatic PCET and electronically nonadiabatic proton transfer, is given with Equation (1):

 2  el 2 r  G0 + λ  X X V Sµν π  ∆ µν  k = P exp  (1) µ λk T  4λk T  µ ν } B − B  Molecules 2020, 25, 1443 3 of 16

el where µ and ν are reactant and product vibronic states, Pµ is the Boltzmann probability, V is the electronic coupling, Sµν is the overlap between the reactant and product vibrational wavefunctions, λ is the reorganization energy, ∆Gºµν is the reaction free energy. The equation is expanded by including the proton donor-acceptor motion, R-mode, characterized by oscillator’s eﬀective mass, M and frequency, Ω. Rate expressions in the low-frequency (high-temperature) regime for R-mode, where the energy associated with the R-mode is lower than the thermal energy, h¯ Ω k T, and in high-frequency (low-temperature) regime, for h¯ Ω k T, B B have been derived. Rate expression in low-frequency regime is identical to the rate expression derived by Kutznetsov and Ulstrup and implemented by Klinman and others in the study of enzymatic PCET reactions [8].

2.2. Kinetic Isotope Effects in PCET Reactions Kinetic isotope effect, the change of rate that occurs upon isotopic substitution, is a widely used tool for elucidating a reaction mechanism, particularly in the study of the hydrogen (H+,H ,H ) − • transfer reactions and the role of hydrogen tunnelling (see Section 2.3.) [1–6,55]. Therefore, the analysis of KIE reveals also the fundamental features of PCET reactions [4,6,9–14,47,56–59]. KIE can be used to distinguish between concerted and stepwise PCET reactions. The experimentally observed magnitudes of the KIE in PCET reactions vary widely, from KIE < 2 to very large and even inverse values [10,11,60]. KIE of 13,000 was observed in the PCET reaction of the isomerization of 2,4,6-tri-tert-butylphenyl at low temperature [61]. In PCET reduction of benzoquinone to hydroquinone by various osmium complexes “colossal” KIE-s from 180 to 460 were observed [62,63]. Moreover, in PCET reaction catalysed by enzyme soybean lipoxygenase (SLO), wild type KIE of ~ 80 [64] increased to the values from 553 to 760 in the case of various mutants [7,41,65,66]. Recently, KIE has been used in the study of the excited-state PCET in DNA duplex [67], in concerted proton-coupled interfacial electron transfer [44], and heterogeneous electrochemical PCET reaction [68]. In addition, it has been widely used in the study of enzymatic reactions, many of which are PCET reactions [7,55,64–66,69,70]. The temperature-dependences of KIE in PCET reactions vary from significantly temperature-dependent, to temperature-independent KIE-s [7,19,20,69–71]. This wide span of KIE temperature-dependences, observed in a great number of enzymatic but also in solution PCET reactions are usually interpreted with Marcus like full-tunnelling model (see Section 2.3.) [7,64,72]. In the case of PCET ubiquinol oxidation by cytochrome bc1 even inverse temperature dependence was observed [60]. Within PCET theory (see Section 2.1.) expressions for KIE in two R-mode regimes were derived [13,73]. In low-frequency regime, with assumptions that only ground states contribute to the rate, and reorganization energy and driving force are independent of the isotope, the KIE is given with Equation (2): " # S 2 2k T KIE | H| exp B α2 α2 (2) ≈ S 2 −MΩ2 D − H | D| where S is the overlap between the reactant and product vibrational wavefunctions, M and Ω are effective mass and frequency of proton donor-acceptor oscillator, α represents exponential dependence of overlap on proton donor-acceptor distance, R. The magnitude of the KIE primarily depends on distance and frequency. KIE increases as R increases, if all other parameters are constant, due to the H/D difference in distance dependence of proton vibrational wavefunctions overlap. KIE increases as Ω increases since higher frequency typically does not enable effective sampling of smaller distances. Very often, a decrease of R leads to an increase of Ω leading to the complex dependence of KIE on R. Contributions from excited vibronic states lead to a decrease of the KIE due to the greater overlap of excited states. Moreover, excited states contribute more to the deuterium overall rate, because of the smaller splittings between the energy levels. The theory also predicts the dependence of KIE on temperature, driving force and solvent reorganization energy. KIE decreases with increasing temperature due to the greater contribution Molecules 2020, 25, 1443 4 of 16

of excited states and the temperature-dependence of KIE will increase as the frequency Ω decreases. KIE has the greatest value near zero driving force and decreases as reactions are more endergonic or exergonic, due to increased contributions from excited vibronic states, and also could even become Moleculesinverse 2020 in, 24 the, x invertedFOR PEER regionREVIEW [46 ]. KIE is relatively insensitive to changes in the solvent reorganization4 of 15 energy in the 10 40 kcal/mol range [10,73]. − even becomeIn low-temperature inverse in the inverted (high-frequency) region [46 regime]. KIE is for relatively the R-mode, insensitive as in the to changes case of a in rigid the solvent hydrogen reorganizationbond, KIE is energy given with in the Equation 10−40 kcal/mol (3): range [10,73]. In low-temperature (high-frequency) regime for the R-mode, as in the case of a rigid hydrogen   bond, KIE is given with equation (3): S2  } α2 α2  H  D − H  KIE =2 exp 2 2  (3) 푆 2 ℏ−(훼 −2M훼Ω)  H SD D H KIE = 2 exp [− ] (3) 푆D 2푀훺 KIE increases as R and Ω increase, and is independent of the driving force and temperature KIE increases as R and Ω increase, and is independent of the driving force and temperature when when only the ground states contribute to the rate. Contributions from excited states could lead to only the ground states contribute to the rate. Contributions from excited states could lead to either a either a decrease or an increase of the KIE with temperature, as observed experimentally in the case of decrease or an increase of the KIE with temperature, as observed experimentally in the case of ubiquinol analog oxidation [74]. ubiquinol analog oxidation [74]. Recently, reactive mode composition factor method has been applied to predict KIE and hydrogen Recently, reactive mode composition factor method has been applied to predict KIE and tunnelling in a series of PCET reactions [56]. hydrogen tunnelling in a series of PCET reactions [56]. 2.3. Hydrogen Tunnelling 2.3. Hydrogen Tunnelling + Hydrogen (H ,H−,H ) transfer is one of the most ubiquitous reactions that take place in nature, + − • especiallyHydrogen among (H , H enzyme, H•) transfer catalysed is one reactions of the most [7,8,69 ubiquitous,75,76]. Hydrogen reactions hasthat thetake small place mass in nature, and de especiallyBroglie wavelengthamong enzyme of similar cataly magnitudesed reactions to molecular [7,8,69,75,76] dimensions. Hydrogen or distances has the expectedsmall mass for andhydrogen de Broglietransfer wavelength to occur. Therefore, of similar the magnitude quantum mechanical to molecular behaviour dimensions of hydrogen or distances particle expecte like hydrogend for hydrogentunnelling transfer could to beoccur. expected Therefore, to play the aquantum signiﬁcant mechanical role in hydrogen behaviou transferr of hydrogen reactions particle [3,7 ,like69,77 ]. hydrogenQuantum tunnel mechanicalling could tunnelling be expected of hydrogen to play can a significant occur when role the in wavefunction hydrogen transfer of hydrogen reactions on the [3,7reactant,69,77]. (hydrogen Quantum donor)mechanical overlaps tunnel withling that of of hydrogen the hydrogen can occu on ther when product the (hydrogen wavefunction acceptor) of hydrogen(Figure1 o).n the reactant (hydrogen donor) overlaps with that of the hydrogen on the product (hydrogen acceptor) (Figure 1).

FigureFigure 1. 1.IllustrationIllustration of of the the ground-stateground-state quantum quantum mechanical mechanical tunnelling tunnelling of hydrogen. of hydrogen Black. parabolasBlack parrepresentabolas represent potential potential energy energy (E) curves (E) curves for reactant for reactant and product. and product. The wavefunction The wavefunction of lighter of lighter isotope isotope(protium, (protium, in green) in green) is less is localized less localized due to due a smaller to a smaller mass in mass comparison in comparison to heavier to isotopeheavier (deuterium, isotope (deuterium,in red). Overlap in red). of Overlap reactant’s of and reactant’s product’s and hydrogen product’s wavefunctions hydrogen wave canfunctions lead to H-tunnelling. can lead to H- tunnelling. Tunnelling is very sensitive to the shape (width and height) of the barrier; it can happen well belowTunnel theling barrier is very maximum sensitive in to the the case shape of a (width narrow and barrier height) or close of the to barrier; the top init can the happen case of awell broad belowbarrier the [barrier70,78]. Themaximum early theoretical in the case model of a narrow for hydrogen barrier tunnellingor close to developedthe top in the by Bellcase wasof a basedbroad on barriertunnelling [70,78] correction. The early oftheoretical the semi-classical model for rate hydrogen constant tunnel withinling a developed framework by of Bell the was transition-state based on tunnelling correction of the semi-classical rate constant within a framework of the transition-state theory [3]. The common signatures of hydrogen tunnelling according to Bell model were the values of isotopic Arrhenius prefactor ratios AH/AD and the isotopic differences in activation enthalpies ΔΔH‡ that are well beyond the semiclassical limits [3,5,6]. Although Bell model could explain large and temperature-dependent KIE-s, it failed to explain the temperature-independent KIE-s under room temperature conditions observed in some enzymatic H-transfer reactions [7,8,69,76,79]. Models that can accommodate both temperature-dependent and temperature-independent KIE near room

Molecules 2020, 25, 1443 5 of 16 theory [3]. The common signatures of hydrogen tunnelling according to Bell model were the values of isotopic Arrhenius prefactor ratios Ah/Ad and the isotopic differences in activation enthalpies ∆∆H‡ that are well beyond the semiclassical limits [3,5,6]. Although Bell model could explain large and temperature-dependent KIE-s, it failed to explain the temperature-independent KIE-s under room temperature conditions observed in some enzymatic H-transfer reactions [7,8,69,76,79]. Models that can accommodate both temperature-dependent and temperature-independent KIE near room temperature are full tunnelling models, also known as Marcus-like models [7,69,76,78]. Within this approach, the motion of heavy atoms of donor and acceptor is treated quantum-mechanically. Reorganization of heavy atoms leads to a tunnelling-ready state with transiently degenerate potential energy surfaces of reactants and products that allow for donor-acceptor wavefunctions to overlap. The effect of donor-acceptor distance (DAD) in tunnelling ready state is thoroughly investigated in many enzymatic C–H bond cleavage reactions [7,69,76]. The crucial experimental parameter for H-tunnelling that emerged from such studies is the difference between energies of activation for hydrogen isotopes H and D, ∆Ea = Ea(D) Ea(H), i.e., the temperature dependence of KIE. In many cases, for the most active − wild-type enzymes ∆Ea is nearly 0 (temperature-independent KIE) suggesting that DAD is sufficiently short to ensure effective tunnelling of both H and D isotopes. Impaired enzymes show enlarged values of ∆Ea (temperature-dependent KIE) and poor overlap of deuterium wavefunctions that necessitate further DAD sampling to achieve adequate DAD for tunnelling. This experimentally and theoretically predicted behaviour was recently confirmed and corroborated by high-precision electron nuclear − double resonance (ENDOR) spectroscopy of prototypical nonadiabatic tunnelling system, soybean lipoxygenase [80].

3. Kinetic Isotope Effects and Hydrogen Tunnelling in Ascorbate PCET Oxidations Kinetic isotope effects and hydrogen tunnelling (recall that the transfer of proton and electron in concerted PCET corresponds to “net” hydrogen transfer) have been investigated in the PCET ascorbate oxidations comprising three different reactions and three different cases with respect to the charge bearing the oxidants: 2,2,6,6-tetramethylpiperidine-1-oxyl radical (TEMPO) has no net charge, hexacyanoferrate(III) is negatively and ferricinium ion is positively charged. The choice of the oxidants bearing different charges should also, be related to the donor-acceptor distance (DAD) in a transition configuration in PCET reaction (due to repulsive/attractive forces between the redox partners) since DAD is of great importance for the magnitude of KIE in the reaction [10,13,35,54,73]. Furthermore, the effective barrier width, the crucial factor determining probability of quantum mechanical tunnelling can be in relation to sampling of optimal donor-acceptor distances at the tunnelling-ready state. In the cases examined, repulsive/attractive forces that appear due to charge on the reactants (or are absent when a reactant is uncharged) would influence DAD in a different manner which could be, among others, of significance for the magnitude of DAD in the interaction with negatively charged ascorbate monoanion. The kinetic isotope effects observed in almost all ascorbate PCET systems presented here are increased unexpectedly [17–19,21–23] with regard to the KIE-s observed in particular “neat” water reaction. The only exception is the case of hexacyanoferrate oxidant in more concentrated water solutions of inorganic salts [20] where the observed KIE-s are reduced in magnitude. The most common phenomenon observed throughout all the three investigated PCET reactions of ascorbate including all the solvent/solute added systems, regardless of the organic cosolvent or the salt added in the water reaction solution is the appearance of hydrogen tunnelling. The observed common signatures of hydrogen tunnelling in a reaction, the values of isotopic Arrhenius prefactor ratios Ah/Ad and the isotopic differences in Ea(D,H) or activation enthalpies ∆∆H‡(D,H) that are well beyond semiclassical limits [3,5,6] suggest so-called moderate hydrogen tunnelling in all the cases excepting the more concentrated water solutions of the inorganic salts (keeping in mind, however, ( that Ea(D,H) and ∆∆H‡ (D,H) are not entirely equivalent). In these systems, values of the isotopic differences in activation enthalpies ∆∆H‡(D,H) below the semiclassical limit of 5.1 kJ/mol and the Molecules 2020, 25, 1443 6 of 16

isotopic prefactor ratios Ah/Ad above the upper semiclassical limit of 1.4, indicative of entering into extensive tunnelling where both the isotopes tunnel were observed. Seemingly, in the initial system, the reaction in “neat” water, there could be no obvious tunnelling manifested. However, taking into account the great KIE that is well beyond the semiclassical limits observed in the interaction of ascorbate monoanion and the TEMPO radical in water reaction Moleculessystem 2020 [17,, 1824,], x asFOR well PEER as REVIEW the ∆∆ H‡(D,H) observed in the case, tunnelling should occur in the reaction.6 of 15 The case of interaction of ascorbate with hexacyanoferrate(III) seems to be less clear; however, tunnelling “neat”would water most probablyfits in the occur strong in linear that case correlation too. Thus, of the ln pointAH/AD for and the ΔΔ reactionH‡(D,H) in “neat”that comprise water ﬁts all in the the systemsstrong linear(see Section correlation 3.5.1. of) lnsuggestingAh/Ad and the∆∆ commonH‡(D,H) physical that comprise origin all of the tunnelling systems (see in all Section the cases 3.5.1 .) investigated.suggesting theFurthermore, common physicalthe value origin of ΔΔH of‡(D,H) tunnelling that is in below all the the cases semiclassical investigated. limit of Furthermore, 5.1 kJ/mol inthe that value case of may∆∆H be‡(D,H) viewed that to is belowapproach the semiclassicalthe extensive limit tunnelling of 5.1 kJ regime./mol in thatFinally, case gre mayat be negative viewed entropiesto approach of activ the extensiveation indicative tunnelling of tunnel regime.ling Finally, [81,82 great], are negative observed entropies in all the of activationexamined indicative reaction systemsof tunnelling and the [81 magnitude,82], are observed of the entropy in all the loss examined observed reaction in the “neat” systems water and reactions the magnitude suggest ofs thea compellingentropy loss similarity observed with in the the “neat” values water of activat reactionsion entropy suggests for a the compelling great majority similarity of the with other the systems values of investigated.activation entropy for the great majority of the other systems investigated. TheThe results results of of the the study study of of KIE KIE-s-s and and tunnelling tunnelling in in the the ascorbate ascorbate reactions reactions [11,17 [11,17–23,72–23,72] ]can can contributecontribute to to the the better better understanding understanding of of PCET PCET reactions; reactions; moreover, moreover, many many enzymatic enzymatic reactions reactions involveinvolve PCET. PCET. The The reactions reactions of of ascorbate ascorbate presented presented are are similar similar to to the the reactions reactions cataly catalysedsed by by ascorbate ascorbate peroxidaseperoxidase enzymes enzymes [83], [83], and and cytochrome cytochrome b b561561 proteinsproteins [84], [84 ],being being thus thus a agood good potential potential reference reference solutionsolution reactions reactions which which is is of of importance importance for for the the stud studyy of of enzyme enzyme catalysis. catalysis.

3.1.3.1. Reaction Reaction of ofAscorbate Ascorbate with with TEMPO TEMPO Radical Radical in in the the Mixed Mixed Water Water-Organic-Organic Cosolvent Cosolvent Systems Systems TheThe reaction reaction (Scheme (Scheme 11)) in in water water as as well well as as in in water water-organic-organic cosolvent cosolvent solutions solutions [17,18 [ 17,18] involves] involves PCETPCET in in the the rate rate-controlling-controlling step step where hydrogen fromfrom 2-OH2-OH position position of of ascorbate ascorbate is is transferred transferred to to the theTEMPO TEMPO radical radical and and sizeable sizeabl isotopee isotope eﬀ ectseffects are are observed. observed.

SchemeScheme 1. 1. OxidationOxidation of of ascorbate ascorbate monoanion monoanion with with 2,2,6,6 2,2,6,6-tetramethylpiperidine-1-oxyl-tetramethylpiperidine-1-oxyl (TEMPO (TEMPO))

radical.radical. kHAsckHAsc− is theis the second second-order-order rate rate constant constant for for the the rate rate-controlling-controlling proton proton-coupled-coupled electron electron − transfertransfer (PCET (PCET)) process process (first (ﬁrst step). step).

TheThe KIE KIE-s-s found found for for various solventsolvent systemssystems are are always always well well beyond beyond the the semiclassical semiclassical limit limit of 7–10 of h d 7–expected10 expected for thefor hydrogenthe hydrogen transfer tran fromsfer from an OH an moiety, OH moiety, reaching reaching up to kup/k to ofkH 31/kD inof the31 water-dioxanein the water- dioxanesolvent solvent system atsystem room at temperature room temperature (Table1). (Table The observed 1). The observed isotope e ﬀisotopeects increase effects on increase the decrease on the of decreasesolvent polarity,of solvent going polarity, from thegoing water from reaction the water solution reaction to the solution mixed solventsto the mixed in all solvents the cases in examined. all the casesThis examined. is more obvious This is in more the case obvious of the in series the case of water-dioxane of the series of mixtures water-dioxane where the mixtures increase where of the the KIE increasefollows of roughly the KIE a linearfollows dependence roughly a linear on the dependence molar fraction on ofthe dioxane molar fraction in water of [17 dioxane]. PCET in reactions water [17].can PCET retain reactions some resemblance can retain withsome proton resemblance transfer w reactionsith proton and transfer changes reactions of KIE-s and (and changes the tunnelling of KIE- s signatures) (and the tunnelling on solvent signatures) polarity in proton on solvent transfer polarity reactions in proton are known transfer for decades reactions [3] are but knownno generally for decadesaccepted [3] explanation but no generally of the accepted issue is available. explanation Theoretical of the issue treatments is available. of PCET Theoretical reactions treatments [13,35,54 ,of73 ] PCETcould re explainactions in[13,35,54,73] part the KIE could dependence explain in insofar part the as KIE solvent dependence polarity insofar may inﬂuence as solvent DAD polarity or driving may influenceforce ∆G DAD◦ of the or reaction;driving force however, ΔG° of according the reaction; to the however, theory, no according change of to KIE the duetheory to variation, no change of of the KIEreorganizational due to variation energy of theλ reorganizationalwill be expected. energy λ will be expected.

Table 1. Kinetic isotope effects, activation parameters ΔH‡ and ΔS‡, isotopic differences ΔΔH‡(D,H)

and ΔΔS‡(D,H) and ratios AH/AD in the reaction of ascorbate with TEMPO radical. Adapted from [17] and [18].

Solvent KIE H‡/kJ mol−1 S‡/JK−1 mol−1 H‡/kJ mol−1 S‡/JK−1 mol−1 AH/AD Water 24.2 (0.6) 31.0 (0.4) −134 (2) 9.0 (0.6) 4 (3) 0.6 (0.2) Water a 21.9 (0.2) 33.7 (0.4) −124 (2) 7.0 (0.4) −2 (2) 1.34 (0.15) 1,4-diox:water b 31.1 (1.1) 23.9 (0.2) −151 (1) 8.2 (0.4) −1 (1) 1.2 (0.2) MeCN:water b 25.4 (0.3) 31.1 (0.1) −131 (1) 8.4 (0.4) 2 (2) 0.82 (0.1) MeCN:water a,b 23.3 (0.1) 29.4 (0.3) −133 (1) 11.6 (0.5) 13 (1) 0.22 (0.03)

Molecules 2020, 25, 1443 7 of 16

Table 1. Kinetic isotope eﬀects, activation parameters ∆H‡ and ∆S‡, isotopic diﬀerences ∆∆H‡(D,H) and ∆∆S‡(D,H) and ratios Ah/Ad in the reaction of ascorbate with TEMPO radical. Adapted from [17,18].

∆H /kJ 1 ∆∆H /kJ 1 ‡ ∆S‡/JK− ‡ ∆∆S‡/JK− h d Solvent KIE 1 1 1 1 A /A mol− mol− mol− mol− Water 24.2 (0.6) 31.0 (0.4) 134 (2) 9.0 (0.6) 4 (3) 0.6 (0.2) − Water a 21.9 (0.2) 33.7 (0.4) 124 (2) 7.0 (0.4) 2 (2) 1.34 (0.15) − − 1,4-diox:water b 31.1 (1.1) 23.9 (0.2) 151 (1) 8.2 (0.4) 1 (1) 1.2 (0.2) − − MeCN:water b 25.4 (0.3) 31.1 (0.1) 131 (1) 8.4 (0.4) 2 (2) 0.82 (0.1) − MeCN:water a,b 23.3 (0.1) 29.4 (0.3) 133 (1) 11.6 (0.5) 13 (1) 0.22 (0.03) Molecules 2020, 24, x FOR PEER REVIEW − 7 of 15 a with TEACl 0.5 M; b organic cosolvent:water = 1:1 v/v. Abbreviations are as follows: 1,4-dioxane (1,4-diox); aacetonitrile with TEACl (MeCN); 0.5 M tetraethylammonium; b organic cosolvent:water chloride = (TEACl). 1:1 v/v. Abbreviations are as follows: 1,4-dioxane (1,4- diox); acetonitrile (MeCN); tetraethylammonium chloride (TEACl). The KIE-s well beyond the semiclassical limits observed in the reaction strongly suggest hydrogen The KIE-s well beyond the semiclassical limits observed in the reaction strongly suggest tunnelling in the reaction. This is consistent also with the observed isotopic differences in Arrhenius hydrogen tunnelling in the reaction. This is consistent also with the observed isotopic differences in activation parameters Ea(D) Ea(H) or isotopic differences in activation enthalpy, ∆∆H‡(D,H), that are Arrhenius activation parameters− Ea(D) − Ea(H) or isotopic differences in activation enthalpy, greater than the semiclassically predicted value of 5.1 kJ/mol for the hydrogen transfer from O–H. ΔΔH‡(D,H), that are greater than the semiclassically predicted value of 5.1 kJ/mol for the hydrogen The finding of this isotopic difference, accompanied by the observed isotopic ratios of Arrhenius transfer from O–H. The finding of this isotopic difference, accompanied by the observed isotopic prefactors below the semiclassical limit for Ah/Ad < 0.5 should be viewed to be indicative of the ratios of Arrhenius prefactors below the semiclassical limit for AH/AD < 0.5 should be viewed to be moderate tunnelling in the reaction (Table1). However, in the cases of the water-dioxane solution indicative of the moderate tunnelling in the reaction (Table 1). However, in the cases of the water- as well as the water solution of tetraethylammonium chloride, the ratios AH/AD could be close to dioxane solution as well as the water solution of tetraethylammonium chloride, the ratios AH/AD the lower limit of the “extensive” tunnelling where both of the isotopes tunnel or where deuterium could be close to the lower limit of the “extensive” tunnelling where both of the isotopes tunnel or begins to tunnel (see however discussion in [17]). In addition, quite significant negative entropies of where deuterium begins to tunnel (see however discussion in [17]). In addition, quite significant activation are indicative of attainment of transition configuration well organized for tunnelling [81,82]. negative entropies of activation are indicative of attainment of transition configuration well Interestingly, the reaction barriers, ∆G , in the reaction performed in quite various solvent systems organized for tunnelling [81,82]. Interestingly,‡ the reaction barriers, ΔG‡, in the reaction performed differ one from another for 1–2 kJ/mol only, while the isotopic ratios of the Arrhenius prefactors suggest in quite various solvent systems differ one from another for 1–2 kJ/mol only, while the isotopic ratios significant differences in tunnelling. The isotopic differences in activation enthalpy, ∆∆H (D,H) greater of the Arrhenius prefactors suggest significant differences in tunnelling. The isotopic ‡differences in than 5.1 kJ/mol do not invoke an explanation using the Bell tunnelling correction approach [23,70]. activation enthalpy, ΔΔH‡(D,H) greater than 5.1 kJ/mol do not invoke an explanation using the Bell An explanation of the observed tunnelling that will take into account dynamical features of the system tunnelling correction approach [23,70]. An explanation of the observed tunnelling that will take into following a Marcus-like tunnelling model and the context of ideas on “environmentally assisted account dynamical features of the system following a Marcus-like tunnelling model and the context tunnelling” [69] has been suggested [18]. of ideas on “environmentally assisted tunnelling” [69] has been suggested [18]. 3.2. Reaction of Ascorbate with Hexacyanoferrate(III) in the Mixed Water-Organic Cosolvent Systems 3.2. Reaction of Ascorbate with Hexacyanoferrate(III) in the Mixed Water-Organic Cosolvent Systems In the reaction (Scheme2) performed in the “neat” water moderate kinetic isotope e ffect kh/kd of In the reaction (Scheme 2) performed in the “neat” water moderate kinetic isotope effect kH/kD of 4.6 and values Ah/Ad of 0.97 and ∆∆H‡(D,H) of 3.9 kJ/mol have been observed [19,20]. 4.6 and values AH/AD of 0.97 and ΔΔH‡(D,H) of 3.9 kJ/mol have been observed [19,20].

Scheme 2. Oxidation of ascorbate monoanion with hexacyanoferrate(III) ion. kHAsc is the second-order − rate constant for the rate-controlling PCET process (ﬁrst step). Scheme 2. Oxidation of ascorbate monoanion with hexacyanoferrate(III) ion. kHAsc− is the second-order rateSurprisingly constant for great the rate changes-controlling of the PCET KIE-s process and the (first tunnelling step). signatures observed have taken place by adding organic cosolvents into water reaction system (Table2). Surprisingly great changes of the KIE-s and the tunnelling signatures observed have taken place by adding organic cosolvents into water reaction system (Table 2).

Table 2. Kinetic isotope effects, activation parameters ΔH‡ and ΔS‡, isotopic differences ΔΔH‡(D,H) and ΔΔS‡(D,H) and ratios AH/AD in the reaction of ascorbate with hexacyanoferrate(III) Ions in the mixed water-organic cosolvent systems. Adapted from [19] and [22].

Organic H‡/kJ S‡/JK−1 H‡/kJ S‡/JK−1 Cosolvent:Water = KIE AH/AD mol−1 mol−1 mol−1 mol−1 1:1 v/v MeCN:water 8.25 (0.09) 24.8 (0.3) −137.3 (1.0) 6.9 (0.4) 5.9 (1.5) 0.49 (0.09) MeCN:water a 6.55 (0.05) MeCN:water b 6.70 (0.27) MeCN:water c 5.86 (0.17) 28.7 (0.2) −104.0 (0.7) 9.1 (0.3) 16.1 (0.9) 0.14 (0.02) MeCN:water d 7.81 (0.17) 1,4-diox:water 7.84 (0.20) 37.6 (0.2) −99.0 (0.7) 12.7 (0.4) 25.6 (1.4) 0.046 (0.008) 1,4-diox:water e 5.75 (0.14) 35.3 (0.2) −80.8 (0.8) 10.9 (0.3) 22.1 (1.0) 0.07 (0.01) 1,4-diox:water c 4.39 (0.13) 35.5 (0.3) −76.5 (1.2) 8.6 (0.6) 16.5 (2.0) 0.14 (0.03) EtOH:water 7.90 (0.22) 26.4 (0.2) −136.0 (0.7) 11.9 (0.4) 22.7 (1.2) 0.065 (0.010)

Molecules 2020, 25, 1443 8 of 16

Table 2. Kinetic isotope eﬀects, activation parameters ∆H‡ and ∆S‡, isotopic diﬀerences ∆∆H‡(D,H) and ∆∆S‡(D,H) and ratios Ah/Ad in the reaction of ascorbate with hexacyanoferrate(III) Ions in the mixed water-organic cosolvent systems. Adapted from [19,22].

Organic ∆H /kJ ∆S /JK 1 ∆∆H /kJ ∆∆S /JK 1 Cosolvent:Water KIE ‡ ‡ − ‡ ‡ − Ah/Ad mol 1 mol 1 mol 1 mol 1 = 1:1 v/v − − − − MeCN:water 8.25 (0.09) 24.8 (0.3) 137.3 (1.0) 6.9 (0.4) 5.9 (1.5) 0.49 (0.09) − MeCN:water a 6.55 (0.05) MeCN:water b 6.70 (0.27) MeCN:water c 5.86 (0.17) 28.7 (0.2) 104.0 (0.7) 9.1 (0.3) 16.1 (0.9) 0.14 (0.02) − MeCN:water d 7.81 (0.17) 1,4-diox:water 7.84 (0.20) 37.6 (0.2) 99.0 (0.7) 12.7 (0.4) 25.6 (1.4) 0.046 (0.008) − 1,4-diox:water e 5.75 (0.14) 35.3 (0.2) 80.8 (0.8) 10.9 (0.3) 22.1 (1.0) 0.07 (0.01) − 1,4-diox:water c 4.39 (0.13) 35.5 (0.3) 76.5 (1.2) 8.6 (0.6) 16.5 (2.0) 0.14 (0.03) − EtOH:water 7.90 (0.22) 26.4 (0.2) 136.0 (0.7) 11.9 (0.4) 22.7 (1.2) 0.065 (0.010) − Acetone:water 8.59 (0.13) a 0.1 M Na-acetate; b 0.1 M NaCl; c 0.1 M KCl; d MeCN:water = 0.25:0.75 v/v; e 0.3 M NaCl. Abbreviations are as follows: 1,4-dioxane (1,4-diox); acetonitrile (MeCN); ethanol (EtOH).

Thus, KIE-s in 1:1 water-cosolvent systems are nearly twice the figure in “neat” water system and very pronounced tunnelling signatures, isotopic ratios of the Arrhenius prefactors and the isotopic differences in activation enthalpy are observed. While according to the theory, an increase of KIE-s could be expected on going from the water reaction solution to the mixed solvents employed due to an increase of DAD with the decrease of solvent polarity (when both the reactants are negatively charged, see also above and Section 2.2.), inspection of KIE-s in Table2 should suggest that other factors also are involved. Namely, the polarity of the water-dioxane and water-ethanol systems surely are lower than that of water-acetonitrile solvent, but the KIE observed in water-acetonitrile is greater than KIE observed in the former two. The theory predicted that KIE-s could increase or decrease owing to a decrease or increase of the reaction driving force ∆G◦. Therefore, an expectation is, that the addition of 3 + the inorganic salts where ion pairs [Fe(CN)6] −,K for example, presumably are formed and driving force should be decreased [23], would lead to an increase of KIE in the reaction. However, the situation is not that simple. In contrast, the addition of 0.1 M KCl lead to the significant decrease of KIE-s in the water-dioxane as well in the water-acetonitrile system (Table2). More interestingly, the observed tunnelling signatures are essentially of the same magnitude in both the cases. Once again, it seems that explanation of the observed intriguing KIE-s and tunnelling should take into account dynamical features of the system, especially those related also to dynamics of solvation shell; this context could perhaps bear few similarities with the dynamical interactions between the hydration shell and bulk and the protein dynamics [85].

3.3. Reaction of Ascorbate with Hexacyanoferrate(III) in More Concentrated Aqueous Solutions of the Salts Two distinct situations appear with regard to the observations of the KIE-s and hydrogen tunnelling in the reaction in water solutions containing various salts. First, when the solutes added are quaternary ammonium salts, sizeable increases of KIE, even close to the semiclassical limit, and the pronounced hydrogen tunnelling signatures characteristic of moderate tunnelling regime have been observed (Table3). Molecules 2020, 25, 1443 9 of 16

Table 3. Kinetic isotope eﬀects, activation parameters ∆H‡ and ∆S‡, isotopic diﬀerences ∆∆H‡(D,H) and ∆∆S‡(D,H) and ratios Ah/Ad in the reaction of ascorbate with hexacyanoferrate(III) ions in more concentrated aqueous solutions of salts. Adapted from [20,21].

∆H /kJ 1 ∆∆H /kJ 1 ‡ ∆S‡/JK− ‡ ∆∆S‡/JK− h d Salt Added KIE 1 1 1 1 A /A mol− mol− mol− mol− KCl 0.5 M 3.37 (0.07) 20.3 (0.2) 121.0 (0.8) 1.8 (0.4) 4.0 (1.2) 1.61 (0.25) − − NaCl 0.5 M 3.78 (0.07) 21.1 (0.4) 121.2 (1.3) 1.3 (0.6) 6.9 (2.1) 2.29 (0.60) − − NaCl 1.0 M 3.31 (0.07) 21.1 (0.2) 118.3 (0.6) 1.5 (0.4) 4.7 (1.3) 1.77 (0.29) − − Na-acetate 0.5 M 3.77 (0.12) LiCl 0.5 M 3.93 (0.18) TEACl 0.5 M 9.49 (0.12) 21.6 (0.3) 131.0 (1.0) 11.1 (0.5) 19.0 (2.2) 0.10 (0.02) − TEACl 1.0 M 10.08 (0.07) TMACl 0.5 M 6.48 (0.08) 15.9 (0.2) 141.0 (1.0) 6.9 (0.3) 8.0 (1.4) 0.35 (0.06) − TMACl 1.0 M 6.79 (0.13) BTMACl 0.5 M 7.53 (0.11) 15.7 (0.2) 141.8 (0.6) 8.6 (0.2) 12.3 (0.8) 0.23 (0.02) − BTMACl 1.0 M 8.01 (0.19) Abbreviations are as follows: tetraethylammonium chloride (TEACl); tetramethylammonium chloride (TMACl); benzyltrimethylammonium chloride (BTMACl).

Second, with regard to the effects of added organic cosolvents, the effects of the added quaternary ions are very similar in the magnitude and direction of the changes of KIE-s and the tunnelling signatures. However, the conspicuous difference between the two classes of solutes added exists; the observed effects of quaternary ammonium ions appear at concentrations that are one order of magnitude lower than in the case of organic cosolvents. This should probably be a consequence of the formation of (likely solvent separated) ion pairs with the hexacyanoferrate(III) ions; then, organic species could be close to the transition reaction configuration at substantially lower concentrations than in the case of uncharged molecules of the cosolvents. Taking into account the above-described cases of salts added into the mixed solvents (cf. Table2 in Section 3.2, the decrease of KIE-s due to ions added) however, the open questions about the role of quaternary ions remain, especially because the species are organic having the charge at the same time. Moreover, the case should be questioned also in the light of effects of inorganic ions added into the same reaction water system (see below), including the solvation/desolvation phenomena too. In the second case, that of inorganic salts added into the water reaction system, quite unexpectedly the decrease of KIE-s and the appearance of hydrogen tunnelling signatures indicative of extensive tunnelling regime have been observed (Table3). Obviously, only the cations from the inorganic salts added have a role in the observed variation of the KIE-s (and the reaction rates too, see in Table3); the influence of anions is insignificant. Since these experiments included only the water solutions, the intriguing transition from the moderate hydrogen tunnelling regime to the extensive tunnelling where both the isotopes tunnel could be traced probably in the differences of solvation of both the hexacyanoferrate(III) anion and inorganic cation in water and in the mixed solvents. Indeed, the above-mentioned cases of the decreased KIE-s in the mixed solvents when the cations are present in the reaction solution (see in Table2), point more to the role of inorganic cations and their solvation/charge density and the differences in ion-ion interactions in the various systems. That is, the interaction with the cations could lead to a more favourable “packaging” of the reactants (due to proximity of cation and the negatively charged transition configuration) thus enabling extensive tunnelling. However, taking into account the tunnelling phenomena observed, there could be one more reason to consider not only bulk solvent properties and ionic effects but dynamical features of the systems as well.

3.4. Reaction of Ascorbate with Ferricinium Ions in Aqueous Solutions of Sodium Chloride The reaction of ascorbate with ferricinium ions [22] involves the interaction of the negatively and the positively charged species. Relative low KIE-s and the ratios of isotopic Arrhenius prefactors Molecules 2020, 25, 1443 10 of 16 signatures consistent with the moderate tunnelling have been observed in the reaction (Table4). While only few data are available, the fact that observed KIE on addition of the inorganic salt increases and the isotopic differences of activation enthalpies are below the semiclassical limit seemingly appears to be at odds with the results presented above (in Section 3.3.). It would be expected that an interplay of different factors, including these related to the water dynamics, could lead to the peculiarities observed in the case. Relatively small loss of the activation entropy could suggest the existence of tight ion pairs consisted of ascorbate and ferricinium ions in the ground state of reaction. A decrease of the (equilibrium) DAD might be expected due to attractive forces between the oppositely charged reactants. Taken together, the observations would be consistent with well organized transition configuration feasible to hydrogen tunnelling in the process.

Table 4. Kinetic isotope eﬀects, activation parameters ∆H‡ and ∆S‡, isotopic diﬀerences ∆∆H‡(D,H) and ∆∆S‡(D,H) and ratios Ah/Ad in the reaction of ascorbate with ferricinium ion. Adapted from [22].

∆H /kJ 1 ∆∆H /kJ 1 ‡ ∆S‡/JK− ‡ ∆∆S‡/JK− h d KIE 1 1 1 1 A /A mol− mol− mol− mol− Water 1.91 (0.02) 45.0 (0.2) 26.0 (0.7) 2.1 (0.3) 1.8 (0.9) 0.80 (0.09) − 0.5 M NaCl 2.01 (0.03) 45.6 (0.1) 32.7 (0.4) 3.4 (0.4) 5.5 (1.5) 0.52 (0.10) − MeCN:water a 1.48 (0.03) a MeCN:water = 1:1 v/v. Abbreviation is as follows: acetonitrile (MeCN).

3.5. Reaction of Ascorbate with Hexacyanoferrate(III) in Fairly Diluted Aqueous Solutions The study of KIE-s and hydrogen tunnelling phenomena in the above PCET reaction (Scheme2) performed in fairly diluted water solutions containing low concentrations of various (inert) partially hydrophobic solutes [23] concentrates on the question of the recent proposal of involvement of the collective excitonic vibrational dynamics in aqueous chemistry [24–27]. The investigation starts from the expectation that these fairly diluted water solutions probably can be considered as a good representation of neat water solutions, since the vibrational excitonic dynamics is critical in neat water [23,25,26]. Furthermore, in the fairly diluted solutions the expectation is that there is no influence of the changes of driving force ∆G◦, or DAD, the parameters that, according to theory [35,54,73] can influence the magnitude of KIE-s observed in more concentrated water solutions [23]; the only relevant system property change that can be at work in the cases will be related to the changes of water dynamics. These changes occur due to presence of hydrogen-bonded partial hydrophobes added. The results are surprising; all the KIE-s obtained are increased significantly and the signatures of hydrogen tunnelling indicative of moderate tunnelling are modulated throughout (for more information see Table 1 in [23]). The strongly linear correlation between common tunnelling signatures (Figure2) points to the common physical origin of the phenomenon in all the cases. In our opinion, the results can be adequately explained by invoking the proposal of the involvement of collective and excitonic vibrational water dynamics in the processes [23]. Molecules 2020, 24, x FOR PEER REVIEW 10 of 15

collective excitonic vibrational dynamics in aqueous chemistry [24–27]. The investigation starts from the expectation that these fairly diluted water solutions probably can be considered as a good representation of neat water solutions, since the vibrational excitonic dynamics is critical in neat water [23,25,26]. Furthermore, in the fairly diluted solutions the expectation is that there is no influence of the changes of driving force ΔG°, or DAD, the parameters that, according to theory [35,54,73] can influence the magnitude of KIE-s observed in more concentrated water solutions [23]; the only relevant system property change that can be at work in the cases will be related to the changes of water dynamics. These changes occur due to presence of hydrogen-bonded partial hydrophobes added. The results are surprising; all the KIE-s obtained are increased significantly and the signatures of hydrogen tunnelling indicative of moderate tunnelling are modulated throughout (for more information see Table 1 in [23]). The strongly linear correlation between common tunnelling signatures (Figure 2) points to the common physical origin of the phenomenon in all the cases. In our Moleculesopinion,2020 the, 25 results, 1443 can be adequately explained by invoking the proposal of the involvement11 of 16 of collective and excitonic vibrational water dynamics in the processes [23].

-0.2

-0.4

neat water -0.6 0.01 M TEACl

-0.8 0.005 M TBACl

) ) 0.005 M TMACl

D A

/ 0.005 M TPACl

H -1

A 0.1 M TEACl ln ln ( -1.2 0.1 M BTMACl 0.1 M AChCl -1.4 0.006 M PQCl2 1,4-diox:water= 0.05:0.95 v/v -1.6 1,4-diox:water = 0.1:0.9 v/v MeCN:water = 0.05:0.95 v/v -1.8 MeCN:water = 0.1:0.9 v/v EtOH:water = 0.1:0.9 v/v -2 3 4 5 6 7 8 9 10 -1 ΔEa(D,H) / kJ mol

FigureFigure 2.2. Correlation between between Δ∆EEa(D,H)a(D,H) and and ln ln AAH/HA/DA. DAbbreviations. Abbreviations as noted as noted in [23]. in [ 23Adapted]. Adapted from from[23]. [23]. 3.5.1. Reaction of Ascorbate with Hexacyanoferrate(III) in Fairly Diluted Aqueous Solutions: 3.5.1. Reaction of Ascorbate with Hexacyanoferrate(III) in Fairly Diluted Aqueous Solutions: Hydrogen Tunnelling and the Vibrational Water Dynamics Connected? Hydrogen Tunnelling and the Vibrational Water Dynamics Connected? The explanation [23] of the observed intriguing modulation of the hydrogen tunnelling (and KIE-s) The explanation [23] of the observed intriguing modulation of the hydrogen tunnelling (and in the reaction in diluted water solutions takes into account the insights obtained from ultrafast 2D IR KIE-s) in the reaction in diluted water solutions takes into account the insights obtained from ultrafast spectroscopy of water [24–33]. Here, several points should be noticed. According to the spectroscopy 2D IR spectroscopy of water [24–33]. Here, several points should be noticed. According to the water vibrations are highly coupled and collective in nature. The OH stretch is not only a local vibration spectroscopy water vibrations are highly coupled and collective in nature. The OH stretch is not only but the coherent vibrational motion involving the stretch-bend coupling that can comprise up to six a local vibration but the coherent vibrational motion involving the stretch-bend coupling that can waters. Furthermore, aside from the intermolecular motions mentioned, it was demonstrated [24,26] comprise up to six waters. Furthermore, aside from the intermolecular motions mentioned, it was that the solute and water modes can be correlated when there is H-bonding between the two. Finally, it was proposed that the coherent coupled vibrational motions that involve the solute and water can contribute to activation processes, which should be of profound importance to understanding water chemistry. The investigated reaction (Scheme2) may present a good model reaction to test the proposal [ 24–26] as the coherent coupled vibrational motions that involve the solute and water can contribute to the dynamics of transition configuration and the modulation of hydrogen tunnelling in the process. The reaction meets conditions required for the model since there is H-bonding between the transition configuration and water in the concerted reaction. Therefore, since the reaction system involves DAD oscillations, the dynamical feature related to hydrogen tunnelling, a modulation of hydrogen tunnelling should be expected when the partially hydrophobic solute is present in the system leading to changes in the vibrational water dynamics [23]; the experimental findings are in line with the expectation. The transition reaction configuration is presented schematically by Figure3. Molecules 2020, 24, x FOR PEER REVIEW 11 of 15

demonstrated [24,26] that the solute and water modes can be correlated when there is H-bonding between the two. Finally, it was proposed that the coherent coupled vibrational motions that involve the solute and water can contribute to activation processes, which should be of profound importance to understanding water chemistry. The investigated reaction (Scheme 2) may present a good model reaction to test the proposal [24–26] as the coherent coupled vibrational motions that involve the solute and water can contribute to the dynamics of transition configuration and the modulation of hydrogen tunnelling in the process. The reaction meets conditions required for the model since there is H-bonding between the transition configuration and water in the concerted reaction. Therefore, since the reaction system involves DAD oscillations, the dynamical feature related to hydrogen tunnelling, a modulation of hydrogen tunnelling should be expected when the partially hydrophobic solute is present in the system leading Moleculesto changes2020 , i25n, 1443the vibrational water dynamics [23]; the experimental findings are in line with12 of the 16 expectation. The transition reaction configuration is presented schematically by Figure 3.

FigureFigure 3.3. SchematicSchematic representationrepresentation ofof transitiontransition conﬁgurationconfiguration inin thethe PCETPCET ascorbateascorbate interactioninteraction withwith hexacyanoferrate(III)hexacyanoferrate(III) ion.ion. AdaptedAdapted fromfrom [[23].23].

TakenTaken together, together, the the picture picture is emerging is emerging where where the water the dynamics water dynamics and tunnelling and tunnelling can be connected. can be Experimentally,connected. Experimentally, this can be seen this through can be the seen observed through modulation the observed of the hydrogen modulation tunnelling of the signatures hydrogen intunnelling the reaction, signatures as illustrated in the reaction, by the strongly as illustrated linear correlation by the strongly of isotopic linear valuescorrelation of Arrhenius of isotopic prefactor values ratios ln Ah/Ad and isotopic differences in activation enthalpies ∆∆H‡(D,H) comprising all the cases of of Arrhenius prefactor ratios ln AH/AD and isotopic differences in activation enthalpies ΔΔH‡(D,H) thecomprising fairly diluted all the water cases systems of the fairly (Figure diluted2)[23 ].water systems (Figure 2) [23]. 4. Conclusions 4. Conclusions The most intriguing insights obtained from the studies of KIE-s and the modulation of hydrogen The most intriguing insights obtained from the studies of KIE-s and the modulation of hydrogen tunnelling phenomena in the PCET reactions of ascorbate should be related to the experiments tunnelling phenomena in the PCET reactions of ascorbate should be related to the experiments performed in the diluted water solutions of inert partial hydrophobes; the obtained results should be performed in the diluted water solutions of inert partial hydrophobes; the obtained results should be viewed to confirm the proposal of far-reaching importance [24,26] related to involvement of vibrational viewed to confirm the proposal of far-reaching importance [24,26] related to involvement of water dynamics in activation processes. vibrational water dynamics in activation processes. The experiments strongly suggest the common physical origin of the phenomenon through the The experiments strongly suggest the common physical origin of the phenomenon through the correlation between the obtained hydrogen tunnelling signatures in all the cases. correlation between the obtained hydrogen tunnelling signatures in all the cases. These insights could perhaps be applied, at least in part and along with the explanations that These insights could perhaps be applied, at least in part and along with the explanations that used the theory of PCET reactions, to the cases of KIE-s and hydrogen tunnelling observed in the used the theory of PCET reactions, to the cases of KIE-s and hydrogen tunnelling observed in the reactions in the more concentrated aqueous solutions, as the strong stretch-intermolecular mode reactions in the more concentrated aqueous solutions, as the strong stretch-intermolecular mode coupling, critical for excitonic nature of OH stretch in water, could be seen in a more concentrated salt coupling, critical for excitonic nature of OH stretch in water, could be seen in a more concentrated solution [26]. salt solution [26]. Not insignificant with regard to the insight in the nature of partial hydrophobes, the investigation Not insignificant with regard to the insight in the nature of partial hydrophobes, the of tunnelling in the case described will be of importance for better understanding its role in many investigation of tunnelling in the case described will be of importance for better understanding its situations where hydrophobic species could be relevant to hydrogen transfer/tunnelling process. role in many situations where hydrophobic species could be relevant to hydrogen transfer/tunnelling Authorprocess. Contributions: Conceptualization, S.U.; methodology, A.K.M., C.J.B., V.P.; software, V.P.; validation, A.K.M., C.J.B, and V.P.; investigation, A.K.M., C.J.B., and S.U.; data curation, A.K.M.; writing—original draft preparation, S.U., C.J.B., A.K.M.; writing—review and editing, A.K.M., C.J.B., V.P. and S.U.; visualization, A.K.M., V.P.; supervision, S.U. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Ministry of Science and Education of The Republic of Croatia (006-0063082-0354). Acknowledgments: We thank the Ministry of Science and Education of The Republic of Croatia for support. Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Molecules 2020, 25, 1443 13 of 16

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